The number of values of $x$ for which $sin\,\, 2x + cos\,\, 4x = 2$ is

If $\cos ec\,\theta  = \frac{{p + q}}{{p – q}}$ $\left( {p \ne q \ne 0} \right)$, then $\left| {\cot \left( {\frac{\pi }{4} + \frac{\theta }{2}} \right)} \right|$ is equal to

If $A + B + C = \pi$ & $sin\, \left( {A\,\, + \,\,\frac{C}{2}} \right) = k \,sin,\frac{C}{2}$ then $tan\, \frac{A}{2} \,tan \, \frac{B}{2}=$

If $\cos 2\theta = (\sqrt 2 + 1)\,\,\left( {\cos \theta – \frac{1}{{\sqrt 2 }}} \right)$, then the value of $\theta $ is

The sum of solutions in $x \in (0,2\pi )$ of the equation, $4\cos (x).\cos \left( {\frac{\pi }{3} – x} \right).\cos \left( {\frac{\pi }{3} + x} \right) = 1$ is equal to